29.24.10 problem 672

Internal problem ID [5263]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 672
Date solved : Monday, January 27, 2025 at 10:50:39 AM
CAS classification : [_separable]

\begin{align*} x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 14

dsolve(x^3*(1+y(x)^2)*diff(y(x),x)+3*x^2*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {1}{\sqrt {\frac {1}{\operatorname {LambertW}\left (\frac {c_{1}}{x^{6}}\right )}}} \]

✓ Solution by Mathematica

Time used: 3.424 (sec). Leaf size: 46

DSolve[x^3(1+y[x]^2)D[y[x],x]+3 x^2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {W\left (\frac {e^{2 c_1}}{x^6}\right )} \\ y(x)\to \sqrt {W\left (\frac {e^{2 c_1}}{x^6}\right )} \\ y(x)\to 0 \\ \end{align*}